A new algorithm for solving nonlinear boundary value problems

Abstract

Purpose

The purpose of this paper is to present a new algorithm for solving nonlinear boundary value problems (BVPs).

Design/methodology/approach

The method converts the nonlinear BVP into a system of nonlinear equations. By solving the system, the solution can be determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use and highly accurate.

Findings

The proposed technique allows us to obtain an approximate solution in a series form which satisfies all the given conditions. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear differential equations with initial and boundary conditions.

Originality/value

The paper provides a reliable technique which avoids the tedious work needed by classical techniques and existing numerical methods and does not require discretization in order to find the solutions of the given problems.

Citation

Ben Zitoun, F. and Cherruault, Y. (2009), "A new algorithm for solving nonlinear boundary value problems", Kybernetes, Vol. 38 No. 5, pp. 681-697. https://doi.org/10.1108/03684920910962579